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        <td class="header">&nbsp; Polarimetric Speckle Filter</td>
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<h3>Polarimetric Speckle Filter Operator</h3>

<p>SAR images have
    inherent salt and pepper like texturing called &#8216;speckle&#8217; which degrades
    the quality of the image and makes interpretation of features more
    difficult. The presence of speckle intensity fluctuations in
    single-look complex SAR imagery is an inevitable consequence of the
    nature of coherent image formation. Each radar resolution cell contains
    multiple individual scatters, each of which contributes to the overall
    signal returned from the resolution cell. Since the radar wavelength is
    normally much smaller than the size of the resolution cell, the phase
    obtained from each individual scatterer is effectively random. The
    signals from each scatter may be summed according to the principle of
    superposition, which results in constructive and destructive
    interference. Cells where destructive interference dominates will
    appear to have a low reflectivity, while cells where constructive
    interference dominates will appear to have a high reflectivity. This
    leads to the phenomenon of speckle. It may be shown thatthe speckle
    intensity is exponentiallydistributed.</p>

<p>While the presence of
    speckle in a SAR image can impair qualitative interpretation of the
    image, speckle is even more problematic when interpreting SAR data in a
    quantitative manner. In particular, the reliability of image
    segmentation techniques is adversely-effected by the presence of
    speckle.</p>

<p>For polarimetric SAR data, the speckle filtering is
    based on incoherent averaging and requires handling statistical second
    order representations. Thus the speckle filtering is applied to
    covariance or coherency matrix.</p>

<p>This operator provides the following polarimetric speckle filterings:</p>
<ul>
    <li>Box Car filter</li>
    <li>Refined Lee flter</li>
    <li>IDAN filter<br>
    </li>
    <li>Improved Lee Sigma filter<br>
    </li>
</ul>
<h4>Box Car Filter</h4>

<p>The
    box car filter is a direct application of the incoherent averaging of
    the covariance/coherency matrix over pixels in a neighborhood defined
    by a sliding window. The boxcar filter presents the best filtering
    performance over homogeneous areas. However there are two major
    drawbacks with the box car filter:</p>
<ul>
    <li><span style="color: red;"></span>the sharp edges are generally blurred</li>
    <li><span style="color: rgb(0, 153, 0);"></span>point scatterers are over filtered and transformed to spread targets
    </li>
</ul>
&nbsp;&nbsp;&nbsp; The refined Lee filter introduced below does not have these limitations.<br><h4>Refined Lee
    Filter</h4>

<p>The
    refine Lee filter in [1] is a minimum mean square error (MMSE) filter and was
    developed based on the multiplicative noise model. One major deficiency
    with the MMSE filter is that speckle noise near strong edges is not
    adequately filtered. To compensate this problem, &nbsp;the refined Lee
    filter uses a nonsquare window to match the direction of edges. The
    filter operated in a 7x7 (or 9x9, 11x11) sliding window. One of eight
    edge-aligned windows&nbsp;is selected to filter the center pixel. Only
    the pixels&nbsp;in the non-edge area&nbsp;in the&nbsp;edge-aligned
    window are used in the filtering computation.</p>

<p>The filter follows&nbsp;three major processing steps as given below:</p>
<ul>
    <li><span style="font-style: italic;">Edge-aligned window selection</span>: For each pixel,&nbsp;span image is used
        in selecting the&nbsp;edge-aligned window.
    </li>
    <li><span style="color: rgb(0, 153, 0);"></span><span style="font-style: italic;">Filtering weight computation</span>: The local statistical filter is applied to
        the span image to compute the weight <span style="font-style: italic;">b</span>.
    </li>
    <li><span style="color: rgb(51, 51, 255);"></span><span style="font-style: italic;">Filter the covariance matrix</span>: The same weight <span style="font-style: italic;">b</span> (a scalar) and the same selected window are used to filter each element
        of&nbsp;matrix, <span style="font-style: italic;">Z</span>, independently and equally. The filtered&nbsp;matrix
        is then given by
    </li>
</ul>
<div style="margin-left: 40px;"><img style="width: 145px; height: 32px;" alt="" src="images/polarimetricSpeckleFilterOp_eq1.jpeg"></div>
<p>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; where<span style="text-decoration: underline;"></span></p>

<p style="margin-left: 40px;"><img style="width: 22px; height: 29px;" alt="" src="images/polarimetricSpeckleFilterOp_eq2.jpeg"></p>

<p style="margin-left: 40px;">is the local mean of&nbsp;matrices computed with pixels in the same edge-directed
    window.<br></p><span style="font-style: italic;"></span>
<h4>IDAN Filter</h4>

<p>Conventional filtering method selects pixels from homogeneous areas
    in a fixed size sliding window.&nbsp; The drawback with this approach
    is that the number of pixels selected may not be sufficient to reduce
    the estimation variance.&nbsp; Instead of limiting&nbsp; the pixel
    selection in a fixed size window, the IDAN (Intensity-Driven
    Adaptive-Neighborhood) filter proposed in [2] selects pixels with region growing
    techniques and criteria of the Lee sigma filter. In this algorithm, an
    adaptive neighborhood is determined for each pixel by a region growing
    technique. The pixel is then filtered with the MMSE filter computed
    using all selected pixels. The region growing technique consists of two
    stages:<br>
</p>
<ul>
    <li>In stage 1, pixels within one sigma range are selected. This is the initial growing.</li>
    <li>In stage 2, pixels that are rejected in the initial growing are
        re-examined.&nbsp; Pixels that are within two sigma range are also
        selected in the final adaptive neighborhood. <br>
    </li>
</ul>
<h4>Improved Lee Sigma Filter</h4>

<p>The Lee Sigma filter proposed in [4] assumes Gaussian noise
    distribution and filters the center pixel in a sliding window with the
    average of pixels within the two-sigma range. One major drawback of the
    algorithm is that the mean of pixels within the two-sigma range is
    always underestimated due to the fact that the noise distributions are
    not symmetric and the symmetric thresholds are used in the pixel
    selection. The new Lee Sigma filter [3] extends and improves the Lee
    Sigma filter in the following aspects:<br>
</p>

<ul>
    <li> The bias problem is solved by redefining the sigma range based on the speckle probability density functions.
    </li>
    <li>A target signature preservation technique is developed to prevent point target from being filtered.</li>
    <li>The minimum-mean-square-error (MMSE) estimator is used for adaptive speckle reduction.<br>
    </li>
</ul>

<h4>Input and Output</h4>
<ul>
    <li>The
        input to this operator can be full polarimetric data, it can also be covariance or coherency
        matrix produced by Polarimetric Matrix Generation operator.
    </li>
    <li>The output of this operator is the&nbsp;corresponding filtered matrix.</li>
</ul>
<ol>
</ol>
<h4>Parameters Used</h4>&nbsp;&nbsp; For box car filter, the following processing parameters are used&nbsp;by the
operator (see Figure 1):<br>
<ul>
    <li>Speckle Filter:&nbsp; the box car speckle filter</li>
    <li>Filter Size: the dimension of the sliding window used in averaging covariance/coherency matrix</li>
</ul>
<br>
<img style="width: 450px; height: 450px;" alt="" src="images/speckleFilterDialog1.jpg"><br><br>

<div style="text-align: left;">&nbsp;&nbsp;&nbsp;
    &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;Figure 1. Dialog box for Box Car Speckle Filter<br></div>
<br><br>For refined Lee filter, the following parameters are needed (see Figure 2):<br>
<ul>
    <li>Speckle Filter: the refined Lee speckle filter</li>
    <li>Number of Looks: the number of looks of SAR data, which is used in estimating the speckle&nbsp;noise standard
        deviation
    </li>
    <li>Window Size: the dimension of the edge-aligned window, possible values are 7x7, 9x9 and 11x11</li>
</ul>
<img style="width: 450px; height: 450px;" alt="" src="images/speckleFilterDialog2.jpg"><br><br>&nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Figure 2. Dialog box for Refined Lee Speckle Filter<br>

<p><br>
</p>

<p>For refined Lee filter, the following parameters are needed (see Figure 3):<br>
</p>
<ul>
    <li>Speckle Filter: the IDAN filter</li>
    <li>Number of Looks: the number of looks of SAR data, which is used in estimating the speckle&nbsp;noise standard
        deviation
    </li>
    <li>Adaptive Neighbourhood Size: the maximum number of pixels in the adaptive neighbourhood</li>
</ul>
<p><img style="width: 450px; height: 450px;" alt="" src="images/speckleFilterDialog3.jpg"><br>
</p>

<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Figure 3. Dialog box for IDAN Speckle Filter<br>

</p>

<p><br>
</p>

<p>For Lee Sigma filter, the following parameters are needed (see Figure 4):<br>
</p>

<ul>
    <li>Speckle Filter: the Lee Sigma filter</li>
    <li>Number of Looks: the number of looks of SAR data, which is used in estimating the speckle&nbsp;noise standard
        deviation
    </li>
    <li>Sigma: <br>
    </li>
    <li>Filter Window Size: <br>
    </li>
    <li>Target Window Size: <br>
    </li>
</ul>

<br>

<p><img style="width: 450px; height: 450px;" alt="" src="images/speckleFilterDialog4.jpg"><br></p>

<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Figure 4. Dialog box for Improved Lee Sigma Speckle Filter<br>

</p>

<p><br>
</p>

<p> Reference:&nbsp;</p>

<p>[1] Jong-Sen Lee and Eric Pottier, Polarimetric Radar Imaging: From Basics to Applications, CRC Press, 2009</p>

<p>[2] G. Vasile, E. Trouve, J.S. Lee and V. Buzuloiu,
    "Intensity-Driven Adaptive-Neighborhood Technique for Polarimetric and
    Interferometric SAR Parameters Estimation", IEEE Transaction on
    Geoscience and Remote Sensing, Vol. 44, No. 6, June 2006.</p>

<p>[3] J.S. Lee, J.H. Wen, T.L. Ainsworth, K.S. Chen and A.J. Chen,
    "Improved Sigma Filter for Speckle Filtering of SAR Imagery", IEEE
    TRansaction on Geoscience and Remote Sensing, Vol. 47, No. 1, Jan. 2009.</p>

<p>[4] J.S. Lee, &#8220;Digital image smoothing and the sigma filter,&#8221;
    Comput. Vis. Graph. Image Process., vol. 24, no. 2, pp. 255&#8211;269, Nov.
    1983.<br>
    <br>
</p>

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